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Projective curvature tensor in 3-dimensional connected trans-Sasakian manifolds. (English) Zbl 1365.53030

Summary: The object of the present paper is to study \(\xi\)-projectively flat and \(\phi\)-projectively flat 3-dimensional connected trans-Sasakian manifolds. Also we study the geometric properties of connected trans-Sasakian manifolds when it is projectively semi-symmetric. Finally, we give some examples of a 3-dimensional trans-Sasakian manifold which verifies our result.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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